1. 1. The number of eggs is a multiple of 3, 7 and 9, and 7×9=63 (find the least common multiple).

2. Secondly, the mantissa of the number of eggs is 9, so 63×3, 63× 13, 63×23, 63×23= 1449 meet the requirements.

So the minimum number of eggs is 1449.